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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p>For the IVP with linear ODEs in variable coefficients,</p>
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\begin{equation*}
ty''-ty'+y=2,\qquad y(0)=2, ~~y'(0)=-4.
\end{equation*}
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<p class="continuation">We have <span class="process-math">\({\mathcal L}[y']=sY(s)-y(0)\text{,}\)</span> then <span class="process-math">\({\mathcal L}[ty']=-\frac{\textrm{d}}{\textrm{d}s}[sY(s)-y(0)]=-[Y(s)+sY'(s)]\text{.}\)</span></p>
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